Real polynomials \(\lbrace \phi _n(x)\rbrace _{n=0}^{\infty }\)  with \(\phi _n(x)\) 
of degree \(n\)  which are orthonormal on an interval of the real
line (with respect to some nonnegative weight function)
necessarily satisfy a three-term recurrence relation (see Chapter
10 of [1]}, for example). These relations can be written in the form
\( x \phi _j(x)=\alpha _j \phi _{j+1}(x) +\beta _j \phi _j(x) +\gamma _j\phi _{j-1}(x), \quad \quad j=0,1,\ldots , \) 
